AP EAMCET · Maths · Complex Number
If \(z_1=2+3 i, z_2=4-5 i\) and \(z_3\) are are three points in the Argand plane such that \(5 \mathrm{z}_1+\mathrm{xz}_2+\mathrm{yz}_3=0\) \((x, y \in \mathbb{R})\) and \(z_3\) is the midpoint of the segment joining the points \(\mathrm{z}_1\) and \(\mathrm{z}_2\) then \(\mathrm{x}+\mathrm{y}=\)
- A \(-5\)
- B \(0\)
- C \(4\)
- D \(-1\)
Answer & Solution
Correct Answer
(A) \(-5\)
Step-by-step Solution
Detailed explanation
\(z_3=\frac{z_1+z_2}{2}=3-i\) Now, \(5 z_1+x z_2+\mathrm{yz}_3=0\) \[ \begin{aligned} & \Rightarrow(10+4 x+3 y)+i(15-5 x-y)=0 \\ & \Rightarrow 4 x+3 y=-10 \ldots \text { (i) and } 15-5 x-y=0 \ldots \end{aligned} \] From equations (i) and (ii), we get \(x=5, y=-10\)…
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